The Vietnam War is largely understood as a disaster that the United States should have either avoided or, on the other hand, gone into full throttle and "won." Hindsight is 20/20, meaning that it is easy to see what should or shouldn't have been done after one knows the outcome of an event, but even at the time, the US had the example of the failed French attempts to subjugate the country as a warning of the difficulties of fighting the Vietnamese on their own turf.
However, the United States was very concerned with winning the Cold War. A large part of the US military strategy was based on a policy called containment. While the USSR and China wanted to spread communism across the globe, the US wanted to stop it in its tracks. Therefore, the US was willing to get militarily involved in even minor countries, such as Vietnam, hoping that if it could halt the spread of communism there, communism would not infiltrate neighboring countries. The US very much did not want to see all of Southeast Asia come under communist influence.
Now, a half century or more later, we can see clearly that the United States underestimated the determination of the Viet Cong, the communist fighters, to hold their country against foreign invaders. They knew the terrain better than the US soldiers did, were good fighters, and would stop at nothing to expel the foreigners. While the US also had brave and competent warriors, the stakes were not the same, and the US side of the war was often mismanaged at the top.
The war was also arguably a mistake because of the serious unrest it caused at home. People did not want to be drafted to fight in this war and growing reports of lies and atrocities made some Americans lose faith in their government, ironically allowing socialist and communist groups an opening for recruiting young people in the United States itself.
The American involvement in Vietnam is widely considered to have been unjustified and disastrous. The U.S. became involved in the war because in the context of the Cold War, Vietnam was seen as a vital domino in the theory of the "domino effect," in which the conversion of one country in Asia to communism was viewed as liable to tip other countries in the region into communism.
Vietnam, which had long been colonized by France, was occupied by Japan during World War II. In 1945, when the Japanese forces left, Vietnam returned to French control. However, forces within Vietnam called the Viet Minh, which was an independence movement originally supported by the U.S. and China, came to oppose the French. Eventually, the Viet Minh lost American support and were supported by the Chinese.
The French were dispelled from Vietnam after the battle of Dien Bien Phu in 1954, after the U.S. President, Eisenhower, refused to get involved in supporting the French resistance against Vietnamese independence forces. After the French left, Vietnam was divided at the 17th parallel into a communist north and a nominally democratic south supported by the U.S. However, the Viet Minh had forces supporting independence in the south; these forces, called the Viet Cong, supported expelling the American influence in the south. Under President Kennedy, the U.S. sent advisors and supported a South Vietnamese president who quelled dissent by repressive measures.
In 1964, when the USS Maddox was blown up in the Gulf of Tonkin, the U.S. Congress passed the Gulf of Tonkin Resolution, allowing President Johnson broad latitude to fight in Vietnam without declaring war. During the Vietnam War, which was escalated under Johnson and was finally turned over to the Vietnamese and ended under Nixon, over 50,000 Americans died, and the country returned to communist control with the fall of Saigon in 1975. The war was, therefore, largely a useless effort that also resulted in massive death and destruction in Vietnam. Therefore, the war is widely regarded as a mistake.